A universal framework for non-deteriorating time-domain numerical algorithms in Maxwell's electrodynamics

The project will remove a key difficulty that currently hampers many existing methods for computing unsteady electromagnetic waves on unbounded regions. Numerical accuracy and/or stability may deteriorate over long times due to the treatment of artificial outer boundaries. We propose to develop a universal algorithm and software that will correct this problem by employing the Huygens' principle and lacunae of Maxwell's equations. The algorithm will provide a temporally uniform guaranteed error bound (no deterioration at all), and the software will enable robust electromagnetic simulations in a high-performance computing environment. The methodology will apply to any geometry, any scheme, and any boundary condition. It will eliminate the long-time deterioration regardless of its origin and how it manifests itself. Dr. Tsynkov who co-invented this method is the Academic partner on the project. Phase I included development of an innovative numerical methodology for high fidelity error-controlled modeling of a broad variety of electromagnetic and other wave phenomena. Proof-of-concept 3D computations have been conducted that convincingly demonstrate the feasibility and efficiency of the proposed approach. In Phase II our algorithms will be implemented as robust commercial software tools in a standalone module that can be combined with existing numerical schemes in computational electromagnetic codes.